Quantum Hall Effect and Chern Phases in the 1/5-Depleted Square Lattice

TL;DR

This paper explores how lattice depletion and diagonal hopping in a 1/5-depleted square lattice can induce and control topological phases with quantized Hall conductivities, revealing new regimes of Chern insulators.

Contribution

It demonstrates that introducing diagonal hopping breaks symmetries and enables the engineering of robust Chern insulators in square lattice systems.

Findings

Nonzero total Chern number emerges with diagonal hopping.

Deformation of Hofstadter butterfly spectrum observed.

Parameter regimes identified for optimal topological stability.

Abstract

We investigate the fractional energy spectrum and quantum Hall response of a two-dimensional 1/5-depleted square lattice subjected to a perpendicular magnetic field. Using a tight-binding model that includes both nearest-neighbor (t_1) and next-nearest-neighbor (t_2) hopping, we compute the Hofstadter butterfly and extract quantized Hall conductivities via Chern number calculations. In the absence of diagonal hopping (t_2 =0), the spectrum exhibits exact particle-hole and flux-inversion symmetries, and the total Chern number across all bands vanishes. When t_2 is introduced, these symmetries are broken, the butterfly becomes deformed, new gaps open, and -remarkably-a nonzero total Chern sum can emerge, signaling unconventional topological phases. By systematically varying t_1 and t_2, we identify regimes with large individual Chern indices and parameter windows where gap stability and Hall plateaus are optimized. Our results demonstrated that lattice depletion combined with diagonal hopping provides a tunable route to engineer robust Chern insulators in both artificial and oxide-based square-lattice systems.